The trigonometric ratios can additionally be taken into consideration as functions of a variable which is the measure of an angle.
This edge measure have the right to either be provided in levels or radians . Here, us will usage radians. Since any type of angle with a measure higher than 2 π radians or much less than 0 is identical to some angle through measure 0 ≤ θ 2 π , all the trigonometric functions are regular .
The graph the the sine function looks prefer this:
keep in mind that the domain the the function y = sin ( x ) ) is all genuine numbers (sine is defined for any type of angle measure), the selection is − 1 ≤ y ≤ 1 .
The graph of the cosine role looks like this:
The domain the the duty y = cos ( x ) is all actual numbers (cosine is characterized for any angle measure), the range is − 1 ≤ y ≤ 1 .
The graph of the tangent role looks choose this:
The domain that the function y = tan ( x ) ) is all real numbers other than the values where cos ( x ) is same to 0 , the is, the values π 2 + π n for every integers n . The selection of the tangent duty is all actual numbers.
The graph of the secant role looks favor this:
The domain the the duty y = sec ( x ) = 1 cos ( x ) is again all actual numbers except the worths where cos ( x ) is same to 0 , that is, the worths π 2 + π n for every integers n . The selection of the function is y ≤ − 1 or y ≥ 1 .
The graph the the cosecant role looks like this:
The domain the the role y = csc ( x ) = 1 sin ( x ) is all actual numbers other than the values where sin ( x ) is same to 0 , that is, the values π n for every integers n . The selection of the function is y ≤ − 1 or y ≥ 1 .
The graph of the cotangent role looks like this:
The domain that the function y = cot ( x ) = cos ( x ) sin ( x ) is all genuine numbers other than the values where sin ( x ) is same to 0 , the is, the worths π n for all integers n .
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The variety of the role is all genuine numbers.